Krylov methods have been developed to approximate the solution to shifted linear systems of the same form as (REF ) in many prior works. See, for example, [1]}, [2]}, [3]}, as well as [4]}, where multiple shift-and-invert preconditioners were incorporated to build a rich search space in a GMRES framework, and [5]}, [6]}, where Krylov recycling techniques were utilized to solve shifted linear systems.
